Vlasov Simulations of Trapping and Inhomogeneity in Raman Scattering

We study stimulated Raman scattering (SRS) in laser-fusion conditions with the Eulerian Vlasov code ELVIS. Back SRS from homogeneous plasmas occurs in sub-picosecond bursts and far exceeds linear theory. Forward SRS and re-scatter of back SRS are also observed. The plasma wave frequency downshifts from the linear dispersion curve, and the electron distribution shows flattening. This is consistent with trapping and reduces the Landau damping. There is some acoustic ($\omega\propto k$) activity and possibly electron acoustic scatter. Kinetic ions do not affect SRS for early times but suppress it later on. SRS from inhomogeneous plasmas exhibits a kinetic enhancement for long density scale lengths. More scattering results when the pump propagates to higher as opposed to lower density.Comment: 4 pages, 6 figures. Submitted to "Journal of Plasmas Physics" for the conference proceedings of the 19th International Conference on Numerical Simulation of Plasma

The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Indeterminacy of Spatiotemporal Cardiac Alternans

Cardiac alternans, a beat-to-beat alternation in action potential duration (at the cellular level) or in ECG morphology (at the whole heart level), is a marker of ventricular fibrillation, a fatal heart rhythm that kills hundreds of thousands of people in the US each year. Investigating cardiac alternans may lead to a better understanding of the mechanisms of cardiac arrhythmias and eventually better algorithms for the prediction and prevention of such dreadful diseases. In paced cardiac tissue, alternans develops under increasingly shorter pacing period. Existing experimental and theoretical studies adopt the assumption that alternans in homogeneous cardiac tissue is exclusively determined by the pacing period. In contrast, we find that, when calcium-driven alternans develops in cardiac fibers, it may take different spatiotemporal patterns depending on the pacing history. Because there coexist multiple alternans solutions for a given pacing period, the alternans pattern on a fiber becomes unpredictable. Using numerical simulation and theoretical analysis, we show that the coexistence of multiple alternans patterns is induced by the interaction between electrotonic coupling and an instability in calcium cycling.Comment: 20 pages, 10 figures, to be published in Phys. Rev.

RyR1-targeted drug discovery pipeline integrating FRET-based high-throughput screening and human myofiber dynamic Ca2+ assays.

Elevated cytoplasmic [Ca2+] is characteristic in severe skeletal and cardiac myopathies, diabetes, and neurodegeneration, and partly results from increased Ca2+ leak from sarcoplasmic reticulum stores via dysregulated ryanodine receptor (RyR) channels. Consequently, RyR is recognized as a high-value target for drug discovery to treat such pathologies. Using a FRET-based high-throughput screening assay that we previously reported, we identified small-molecule compounds that modulate the skeletal muscle channel isoform (RyR1) interaction with calmodulin and FK506 binding protein 12.6. Two such compounds, chloroxine and myricetin, increase FRET and inhibit [3H]ryanodine binding to RyR1 at nanomolar Ca2+. Both compounds also decrease RyR1 Ca2+ leak in human skinned skeletal muscle fibers. Furthermore, we identified compound concentrations that reduced leak by > 50% but only slightly affected Ca2+ release in excitation-contraction coupling, which is essential for normal muscle contraction. This report demonstrates a pipeline that effectively filters small-molecule RyR1 modulators towards clinical relevance

Kinetic Enhancement of Raman Backscatter, and Electron Acoustic Thomson Scatter

1-D Eulerian Vlasov-Maxwell simulations are presented which show kinetic enhancement of stimulated Raman backscatter (SRBS) due to electron trapping in regimes of heavy linear Landau damping. The conventional Raman Langmuir wave is transformed into a set of beam acoustic modes [L. Yin et al., Phys. Rev. E 73, 025401 (2006)]. For the first time, a low phase velocity electron acoustic wave (EAW) is seen developing from the self-consistent Raman physics. Backscatter of the pump laser off the EAW fluctuations is reported and referred to as electron acoustic Thomson scatter. This light is similar in wavelength to, although much lower in amplitude than, the reflected light between the pump and SRBS wavelengths observed in single hot spot experiments, and previously interpreted as stimulated electron acoustic scatter [D. S. Montgomery et al., Phys. Rev. Lett. 87, 155001 (2001)]. The EAW is strongest well below the phase-matched frequency for electron acoustic scatter, and therefore the EAW is not produced by it. The beating of different beam acoustic modes is proposed as the EAW excitation mechanism, and is called beam acoustic decay. Supporting evidence for this process, including bispectral analysis, is presented. The linear electrostatic modes, found by projecting the numerical distribution function onto a Gauss-Hermite basis, include beam acoustic modes (some of which are unstable even without parametric coupling to light waves) and a strongly-damped EAW similar to the observed one. This linear EAW results from non-Maxwellian features in the electron distribution, rather than nonlinearity due to electron trapping.Comment: 15 pages, 16 figures, accepted in Physics of Plasmas (2006

Coupled dynamics of voltage and calcium in paced cardiac cells

We investigate numerically and analytically the coupled dynamics of transmembrane voltage and intracellular calcium cycling in paced cardiac cells using a detailed physiological model and its reduction to a three-dimensional discrete map. The results provide a theoretical framework to interpret various experimentally observed modes of instability ranging from electromechanically concordant and discordant alternans to quasiperiodic oscillations of voltage and calcium

Plasmas and Controlled Nuclear Fusion

Contains reports on two research projects.U.S. Atomic Energy Commission (Contract AT(30-1)-3980

Ray-based calculations of backscatter in laser fusion targets

A 1D, steady-state model for Brillouin and Raman backscatter from an inhomogeneous plasma is presented. The daughter plasma waves are treated in the strong damping limit, and have amplitudes given by the (linear) kinetic response to the ponderomotive drive. Pump depletion, inverse-bremsstrahlung damping, bremsstrahlung emission, Thomson scattering off density fluctuations, and whole-beam focusing are included. The numerical code DEPLETE, which implements this model, is described. The model is compared with traditional linear gain calculations, as well as "plane-wave" simulations with the paraxial propagation code pF3D. Comparisons with Brillouin-scattering experiments at the OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, p. 495 (1997)] show that laser speckles greatly enhance the reflectivity over the DEPLETE results. An approximate upper bound on this enhancement, motivated by phase conjugation, is given by doubling the DEPLETE coupling coefficient. Analysis with DEPLETE of an ignition design for the National Ignition Facility (NIF) [J. A. Paisner, E. M. Campbell, and W. J. Hogan, Fusion Technol. 26, p. 755 (1994)], with a peak radiation temperature of 285 eV, shows encouragingly low reflectivity. Re-absorption of Raman light is seen to be significant in this design.Comment: 16 pages, 19 figure